Fraction Multitool

Problem:

Find $\frac{m}{n}$ of $\frac{k}{l} \left( \frac{0}{0} \times \frac{0}{0} \right )$

Explanation:

Partition $\left[ 0 , \frac{k}{l} \right ] ($$\left[ 0 , \frac{0}{0} \right ]$$)$ into $n \left( 0 \right )$ equal parts, then concatenate $m \left( 0 \right )$ of those parts

Solution:

The first step is to partition $\frac{k}{l} \left( \frac{0}{0} \right )$ into $n \left( 0 \right )$ equal parts, but we can't, so we must force $\frac{k}{l} \left( \frac{0}{0} \right )$ into being able to be split into $n \left( 0 \right )$ equal parts. In order to do that, we must use equivalent fractions to make $k \left( 0 \right )$ into a multiple of $n \left( 0 \right )$:

$\frac{k}{l} = \frac{k \times n}{l \times n} = \frac{k n}{\ln{}}$$\frac{0}{0} = \frac{0 \times 0}{0 \times 0} = \frac{0}{0}$

The next step is to split the equivalent fraction into $n \left( 0 \right )$ equal parts, each of which is $\frac{k}{\ln{}} \left( \frac{0}{0} \right )$ in length. All that is left is to concatenate $m \left( 0 \right )$ of these parts.

Answer:

$\frac{m}{n}$ of $\frac{k}{l}$ is $\frac{k \times m}{l \times n}$

$\frac{0}{0} \times \frac{0}{0} = \frac{0}{0}$